Question

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find
(i) $A\text{'}$
(ii) $B\text{'}$
(iii) $\left(A\cap C\right)\text{'}$
(iv) $\left(A\cup B\right)\text{'}$
(v) $\left(A\text{'}\right)\text{'}$
(vi) $\left(B-C\right)\text{'}$

Answer 1

Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B= {2, 4, 6, 8} and C = {3, 4, 5, 6}
(i) $A\text{'}$ = {5, 6, 7, 8, 9}
(ii) $B\text{'}$ = {1, 3, 5, 7, 9}
(iii) $\left(A\cap C\right)\text{'}$ = {1, 2, 5, 6, 7, 8, 9}
(iv) $\left(A\cup B\right)\text{'}$ = {5, 7, 9}
(v) $\left(A\text{'}\right)\text{'}$ = {1, 2, 3, 4} = A
(vi) $\left(B-C\right)\text{'}$ = {1, 3, 4, 5, 6, 7, 9}